190 Mansfield 3ferriman — List cf Writings relating 



These letters are of so elementary a character that S. A. R. is in- 

 formed of the meaning of the signs + and — . They contain how- 

 ever a valuable popular exposition of the Theory of means and of the 

 laws of error. For review of the book see 1850 IIerschel. 



At the end of the book is an appendix containing many valuable 

 " Notes." In pages 375-380 a table of the terms of the binomial 

 ^1. _|_ i^y^"^ for eighty terms on each side of the middle terra is given 

 and the method of its computation explained : these have since been 

 called Quetelet's numbers, see 1869 Galton. In pages 384-387 it 

 is shown that the general tei-m of the binomial (^ -j- ^)'" approaches 

 the exponential form ce~'' ^ as m indefinitely increases : this is sim- 

 ilar to Hagex's investigation of 1837. 



In pages 412-424 are printed three suggestive letters from Bra- 

 vAis, in which not only doubts are expressed as to the d priori 

 necessity of the exponential law of facility of error, but examples 

 are given to show that it is not ixniversally true d posteriori. Bra- 

 vats' view is that every cause of partial error gives rise to a distinct 

 curve of facility and that the combination of these approaches the 

 exponential form as a limit, partly because of the necessary law that 

 positive and negative errors are equally likely, and partly because 

 the combination itself must tend toward the binomial form. He 

 alludes to Hagen's proof as not sufficiently rigorous, 



1847 DeMorgak. 'Theoi-y of Probabilities.' Encycl. of Pure 

 Math. {Encycl. Metrop.), Pt. II, pp. 393-490. 



A great part of this work is translated and adapted from Laplace's 

 Theorie .... des Proh., 1812, enriched by comments. The Method of 

 Least Squares is treated at considerable length according to La- 

 place's method. At the end are given valuable tables, those of 1799 

 Kramp and 1832 Encke, and also factorial tables. 



1847 Galloway. 'Probabilities.' Encycl. Brittanica, seventh 

 ed., Vol. XVIII, pp. 591-639. Eighth edition. Vol. XVIII, pp. 588- 

 636. — Also separately, Edinburgh, 1848, 8vo. 



PoissoTsi's analysis (1824) of Laplace's method is given, and also 

 Gauss's proof of 1823. 



1848 Matzka. 'Beweis des obersten Grundsatzes der Methode der 



kleinsten Quadrate.' Archiv. Math. r«. Phgs., Vol. XI, pp. 369-377. 



A suggestive article. Let ,v be the true value of a quantity for 

 which observations give the values a, ^>, e, . . ., then 



a^=/K ^ ^, ) 



and also we must have 



X — rn =/{a — m, b—nt., c — m,. . . .). 

 Applying Taylor's theorem, Matzka deduces for x 



ha -{- ib -\- kc -\- . . . 



^~ A + *i+ ^ + . . . 



